Find the value
Question:

Find the value

$a^{2}+2 a b+b^{2}-c^{2}$

 

Solution:

Using the identity $(p+q)^{2}=p^{2}+q^{2}+2 p q$

$=(a+b)^{2}-c^{2}$

Using the identity $p^{2}-q^{2}=(p+q)(p-q)$

$=(a+b+c)(a+b-c)$

$\therefore a^{2}+2 a b+b^{2}-c^{2}=(a+b+c)(a+b-c)$

 

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